IEEE Computational Intelligence Magazine - November 2020 - 69

B. Results of Prevention Program Optimization

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The TCM experts develop 15 prevention programs for the 16
clusters of residents (two clusters are very similar and share one
program). Among the 39,720 residents in Hangzhou, 4,625 residents agree to adopt the prevention programs, but medical

resources required to implement the programs significantly
exceed the available resource. Therefore, we use the proposed
WWO algorithm to optimize the programs. Among the 15
updated programs, 13 programs are approved by the experts, and
the remaining two programs are slightly modified by the experts.
The updated programs do not violate the resource constraints
and, therefore, are put into implementation. However, during one
week of implementation, many resources have been consumed,
and the available resources are not sufficient to implement the 15
updated programs. Therefore, we perform a second round of program optimization. Among the 15 programs updated in the second round, 12 programs are approved, and the remaining three
programs are modified by the experts. However, the resources
required by the programs again exceed the available resources.
Therefore, we perform a third round of program optimization,
the results of which are approved and put into implementation.
Among the 9,812 residents in Shaoxing, 1,227 agree to
adopt the prevention programs. In Shaoxing, we perform two
rounds of program optimization, the results of which are put
into implementation successively.
In summary, we use the proposed algorithm to solve five
instances of the prevention program optimization problem. For
comparison, we also implement the following five popular
metaheuristic optimization algorithms on these five instances:
❏❏ The GA for constrained optimization [41];
❏❏ The biogeography-based optimization (BBO) for constrained optimization [42];
❏❏ The DE algorithm for constrained optimization [43];
❏❏ The cuckoo search (CS) algorithm for integer programming [44];
❏❏ The grey wolf optimization (GWO) algorithm for integer
programming [45].

where si is the average distance between each point and the
centroid of cluster i, and dij is the distance between the centroids of clusters i and j.
Fig. 3(a) and (b) compare the performance of the ten clustering algorithms in Hangzhou and Shaoxing, respectively. On
both instances, K-means exhibits the worst performance,
because it aims to minimize the within-cluster sum-of-squares,
but this criterion responds poorly to manifolds with irregular
and uncertain shapes which often exist in population health
data. FCM achieves significant performance advantage over
K-means by incorporating fuzzy logic to effectively deal with
uncertainties [24]. DBSCAN shows similar performance as
FCM, and the standard deviation of DBSCAN over the 30 runs
is smaller. IFCM achieves better results than the standard FCM,
and PFCM achieves better results than IFCM, which shows
that using extended fuzzy sets can improve the fuzzy clustering
by capturing uncertainty information more effectively. Compared to the three basic FCM methods using random initial
cluster centroids, PFCM enhanced by metaheuristic optimization to find optimal/sub-optimal initial centroids achieve significant performance advantages, because the quality of initial
centroids heavily affects the clustering results. Among the five
metaheuristic algorithms, the proposed PFCM-EBO exhibits
the best performance, which demonstrates the efficiency of the
EBO algorithm in optimizing initial centroids for clustering
residents using health data.

(a)

(b)
Q1

Min Median

Max

FIGURE 3 Comparison of the ten algorithms for clustering residents in (a) Hangzhou, and (b) Shaoxing. Each box plot shows the maximum, minimum, median, first quartile (Q1), and third quartile (Q3) of the resulting Davies-Bouldin index values over the 30 runs of an algorithm.

NOVEMBER 2020 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

IEEE Computational Intelligence Magazine - November 2020

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